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Scheme of learning

Standard FormReverse PercentagesSpeed and DensityReal Life and Distance Time GraphsExpanding and Factorising QuadraticsSolving QuadraticsDrawing Quadratic GraphsDrawing Other Graphs: Cubic/Reciprocal

Tests

Test ATest BTest CTest D

Stage 8 Test A

Question 1

Here is the graph of y=x2+2x−3y = x^2 + 2x - 3y=x2+2x−3

Graph of the quadratic function y = x^2 + 2x - 3 on a coordinate plane. The x-axis ranges from -6 to 6 with major grid lines every 2 units and minor grid lines every 1 unit. The y-axis ranges from -6 to 8 with major grid lines every 2 units and minor grid lines every 1 unit. The parabola opens upwards with its vertex at (-1, -4). It crosses the x-axis at (-3, 0) and (1, 0), and the y-axis at (0, -3).

a.

Write down the turning point of the graph y=x2+2x−3y = x^2 + 2x - 3y=x2+2x−3

[1]
b.

Use the graph to find the roots of the equation x2+2x−3=0x^2 + 2x - 3 = 0x2+2x−3=0

[2]
Question 2
a.

Write 8.9 × 10-2 as an ordinary number.

[1]
b.

Work out the value of (4.6×105)×(7.5×103)(4.6 \times 10^5) \times (7.5 \times 10^3)(4.6×105)×(7.5×103) Give your answer in standard form.

[2]
Question 3

In a sale, the normal price of a TV is reduced by 15%. The sale price of the TV is £595

Work out the normal price of the TV.

[2]
Question 4
a.

Expand and simplify (5p−4)(p−2)(5p - 4)(p - 2)(5p−4)(p−2)

[2]
b.

Factorise a2+6a−55a^2 + 6a - 55a2+6a−55

[2]
Question 5
a.

Complete the table of values for y=1x\displaystyle y = \frac{1}{x}y=x1​

xxx0.20.40.8124
yyy
[2]
b.

On the grid, draw the graph of y=1x\displaystyle y = \frac{1}{x}y=x1​

A coordinate grid for graphing the function y = 1/x. The x-axis is labeled 'x' and ranges from 0 to 4 with major grid lines every 1 unit and minor grid lines every 0.2 units. The y-axis is labeled 'y' and ranges from 0 to 6 with major grid lines every 1 unit and minor grid lines every 0.2 units. The origin is labeled 'O'.

[2]
Question 6

Emily drove to the beach. She stayed at the beach and then she drove back home. Here is Emily's travel graph.

A line graph showing distance from home in miles over time. The y-axis is labeled 'Distance from home (miles)' with major grid lines every 10 units and minor grid lines every 2 units. The x-axis is labeled 'Time' with major ticks at 14 00, 14 20, 14 40, 15 00, 15 20, 15 40, and 16 00. The graph starts at (14 00, 0), rises linearly to (14 40, 35), stays horizontal at 35 miles until 15 10, and then falls linearly to (16 00, 0).

TimeDistance from home (miles)
14 000
14 2015
14 4035
15 1035
15 4015
16 000
a.

For how many minutes did Emily stay at the beach?

[1]
b.

What was Emily's average speed on her journey to the beach?

[2]
Question 7

Solve b2−8b+12=0b^2 - 8b + 12 = 0b2−8b+12=0

[3]
Question 8

Liquid A has a density of 1.1 g/ml

150 ml of Liquid A is mixed with some of Liquid B to make Liquid C.

Liquid C has a mass of 378 g and a density of 1.05 g/ml

Find the density of Liquid B.

Give your answer correct to 3 significant figures.

[3]